Once you understand something, you tend to look at it in a completely different light. And you wipe out the memory of how it used to be before. I came across a curious case of this while teaching negative numbers.
The negative numbers carry sign of, - , in front. The sign's job is to suggest the value of the number. The value may be compared to zero, such as -30 or it could be a relative value such as -15 km from my house. The negative sign here is like an adjective.
Unfortunately, the exact same sign, -, is also there for the subtraction operation. Here it represents an operation between two numbers. Namely, the operation of taking difference between the values of two numbers. It is like a verb here. If you can't guess which role the, -, sign is playing then that leads to a great confusion.
Soon things get more complicated. The numbers whose difference is to be taken by subtraction could themselves be positive, +, or negative ,- . Many are unable to recognize the dual role played by, -. This may be one reason why so many children find concept of negative numbers baffling.
It is less confusing if its put in words, such as, "Subtract minus four from three". Here the two jobs played by our friend are clearer. Once you learn to recognize it as an operation or a value, then you see negative numbers in a more generic light.
PS: From another angle, subtraction operation is like finding the value of second number with respect to the first number. But that's even deeper to realize.
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